Questions from General Calculus

Q: Each limit represents the derivative of some function f at some number

Each limit represents the derivative of some function f at some number a. State such an f and a in each case.

Q: If f (x) = x2 + 10 sin x,

If f (x) = x2 + 10 sin x, show that there is a number c such that f (c) = 1000.

Q: (a). Find the slope of the tangent line to the

(a). Find the slope of the tangent line to the curve y = x – x3 at the point (1, 0) (i). using Definition 1 (ii). using Equation 2 (b). Find an equation of the tangent line in part (a). (c). Graph th...

Q: Suppose f is continuous on [1, 5] and the

Suppose f is continuous on [1, 5] and the only solutions of the equation f (x) = 6 are x = 1 and x = 4. If f (2) = 8, explain why f (3) > 6.

Q: Find the horizontal and vertical asymptotes of each curve. If you

Find the horizontal and vertical asymptotes of each curve. If you have a graphing device, check your work by graphing the curve and estimating the asymptotes.

Q: Use the Intermediate Value Theorem to show that there is a root

Use the Intermediate Value Theorem to show that there is a root of the given equation in the specified interval. 3√x = 1 – x, (1, 0)

Q: The number N of US cellular phone subscribers (in millions)

The number N of US cellular phone subscribers (in millions) is shown in the table. (Midyear estimates are given.) (a). Find the average rate of cell phone growth (i). from 2002 to 2006 (ii). from 20...

Q: Use the Intermediate Value Theorem to show that there is a root

Use the Intermediate Value Theorem to show that there is a root of the given equation in the specified interval. sin x = x2 - x (1, 2)

Q: (a). Prove that the equation has at least one real

(a). Prove that the equation has at least one real root. (b). Use your calculator to find an interval of length 0.01 that contains a root. cos x = x3

Q: (a). Graph the function f (x) = ex

(a). Graph the function f (x) = ex + ln |x – 4| for 0 < x < 5. Do you think the graph is an accurate representation of ? (b). How would you get a graph that represents f better?